Ocean tides rise and fall on a sine wave — high water, low water, and back again, roughly every 12 hours and 25 minutes. A sinusoidal function captures any such rhythm with four numbers: y = A·sin(Bx + C) + D, where A is the amplitude (how far it swings), B sets how fast it repeats, C shifts it left or right, and D lifts the whole wave up or down. A tide swinging 3 feet above and below a mean level of 5 feet is y = 3·sin(Bx + C) + 5, and every harbor schedule on the US coast is a dressed-up version of that equation.

The wave's height at any moment comes from multiplying the amplitude by the sine of the angle inside. This calculator performs that multiplication: type the amplitude A in the Variable A box and the sine value in the Variable B box, and the Result box gives the displacement from the midline. For a 3-foot tide amplitude with sin(θ) = 0.5 at some hour, entering 3 and 0.5 returns 1.5 — the water sits 1.5 feet above midline, or 6.5 feet absolute. Add D and you have the reading the tide gauge shows.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Sinusoidal Function Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.